Generally, vulcanized rubber has excellent elasticity in a wide strain range that is not observed in other substances. Therefore, vulcanized rubber is widely used in grease cups, such as automobile dust covers, dust boots, and bellows, in which grease is encapsulated and sealed to prevent entry of dust. Of these, grease cups bonded to supporting bodies made of metal, resin, or the like are required to have excellent adhesion to the supporting bodies. Additionally, with the trends of recent higher-performance engines and smaller-size cars, vulcanized rubber used therein is required to meet rigorous requirements for heat resistance, cold resistance, ozone resistance, and other properties. For example, it is becoming difficult for the rubber compositions disclosed in Patent Documents 1 to 3, described later, to meet these requirements while maintaining satisfactory adhesion to supporting bodies.